trueskill.py

"""
microsoft TrueSkill algorithm for rankings
"""

from __future__ import print_function
import math
import sys

from scipy.stats.distributions import norm as scipy_norm

beta = 25./6
gamma = 25./300
epsilon = 0.08

norm = scipy_norm()

def pdf(x):
    return norm.pdf(x)

def cdf(x):
    return norm.cdf(x)

def Vwin(t, e):
    return pdf(t - e) / cdf(t - e)

def Wwin(t, e):
    return Vwin(t, e) * (Vwin(t, e) + t - e)

def true_skill(winner, loser):
    muw, sigmaw = winner
    mul, sigmal = loser

    c = (2*beta**2 + sigmaw**2 + sigmal**2)**.5
    t = (muw - mul) / c
    e = epsilon / c

    sigmaw_new = (sigmaw**2 * (1 - (sigmaw**2) / (c**2)*Wwin(t, e)) + gamma**2)**.5
    sigmal_new = (sigmal**2 * (1 - (sigmal**2) / (c**2)*Wwin(t, e)) + gamma**2)**.5
    muw_new = (muw + sigmaw**2/c * Vwin(t,e))
    mul_new = (mul - sigmal**2/c * Vwin(t,e))

    winner = muw_new, sigmaw_new
    loser = mul_new, sigmal_new
    return winner, loser


def update(squads, winner, loser):
    winner_stats = squads.get(winner, (25., 25./3))
    loser_stats = squads.get(loser, (25., 25./3))
    squads[winner], squads[loser] = true_skill(winner_stats, loser_stats)


def rank(squads, squad):
    return squads[squad][0] - 3*squads[squad][1]

def main(argv):
    games = [
        ("BARNEY", "STONE") , ("MIXIL", "KANE") , ("KANE", "CUTLER") , ("JOHNSONE", "HUXTABLE") , #day 1
        ("EDISON", "ALI") , ("SHARP", "STEVENS") , ("GALAVANT", "LEVY") , ("BARNEY", "ELROY") , #day 2
        ("MIXIL", "BARNEY") , ("MIXIL", "JOHNSONE") , ("JOHNSONE", "MIXIL") , ("MIXIL", "JOHNSONE") , #day 3
        ("JOHNSONE", "GALAVANT") , ("SALLY", "LEVY") , ("EDISON", "ROSE") , ("POE", "CHEECH") , #day 4
        ("COSTANZA", "HUXTABLE") , ("STONE", "SHARP") , ("KANE", "MIXIL") , ("STEVENS", "KATZ") , #day 5
        ("POE", "COSTANZA") , ("KANE", "STONE") , ("BARNEY", "JETSON") , ("JOHNSONE", "ROBERTSON"), #day 6
        ("POE", "EDISON"), ("NACHE", "KANE") , ("NACHE", "STEVENS") , ("BARNEY", "HO") , #day 7
        ("JOHNSONE", "CUTLER") , ("POE", "NACHE") , ("BARNEY", "JOHNSONE") , ("ELROY", "MARCUS") , #day 8
        ("ROSE", "ELROY") , ("POE", "BARNEY") , ("JOHNSONE", "LEVY") , ("JOHNSONE", "POE") , #day 9
        ("LEVY", "ROSE") , ("ELROY", "SHARP"), ("CHEECH", "MIXIL"), ("MIXIL", "ROSE") , #day 10
        ("SHARP", "HO") , ("JETSON", "MIXIL") , ("ROSE", "ELROY") , ("ROSE", "JETSON") , #day 11
        ("ROSE", "GALAVANT"), ("EDISON", "ROSE") , ("EDISON", "NACHE") , ("NACHE", "STONE") , #day 12
        ("JETSON", "STEVENS") , ("KANE", "SHARP") , ("KANE", "COSTANZA") , ("NACHE", "KANE") ] #day 13

    squads = {}

    for winner, loser in games:
        update(squads, winner, loser)

    for squad in sorted(squads, key=lambda squad: rank(squads, squad),reverse=True):
        mu = squads[squad][0]
        sigma = squads[squad][1]
        print("%6s R: %5.2f mu: %5.2f sigma: %5.2f" % (squad, rank(squads, squad), mu, sigma))

    return 0

if __name__ == "__main__":
    exit_code = main(sys.argv)
    sys.exit(exit_code)